Let p be a prime, and let N be a positive integer coprime to p. Let Mk(Γ1(N);Qp) denote the weight k modular forms of level Γ1(N) defined overQp. In recent years, work of Coleman and others (for example [5],[6],[7],[8],[9]) has shown that a very profitable way of studying this finite-dimensional Qp-vector space is to choose a small positive rational number r and then to embed Mk(Γ1(N);Qp) into ...

Abstract. Let F be a totally real field and p ≥ 3 a prime. If ρ : Gal(F/F ) → GL2(Fp) is continuous, semisimple, totally odd, and tamely ramified at all places of F dividing p, then we formulate a conjecture specifying the weights for which ρ is modular. This extends the conjecture of Diamond, Buzzard, and Jarvis, which required p to be unramified in F . We also prove a theorem that verifies on...

BACKGROUND Intraguild predation (IGP) is widespread but it is often neglected that guilds commonly include many layers of dominance within. This could obscure the effects of IGP making unclear whether the intermediate or the bottom mesopredator will bear higher costs from the emergence of a new top predator. METHODOLOGY/PRINCIPAL FINDINGS In one of the most extensive datasets of avian IGP, we...